Ad
related to: singularity in coordinates meaning in science project proposal pdf format
Search results
Results From The WOW.Com Content Network
An example is the apparent (longitudinal) singularity at the 90 degree latitude in spherical coordinates. An object moving due north (for example, along the line 0 degrees longitude ) on the surface of a sphere will suddenly experience an instantaneous change in longitude at the pole (i.e., jumping from longitude 0 to longitude 180 degrees).
A coordinate singularity occurs when an apparent singularity or discontinuity occurs in one coordinate frame, which can be removed by choosing a different frame. An example of this is the apparent singularity at the 90 degree latitude in spherical coordinates. An object moving due north (for example, along the line 0 degrees longitude) on the ...
Lemaître coordinates are a particular set of coordinates for the Schwarzschild metric—a spherically symmetric solution to the Einstein field equations in vacuum—introduced by Georges Lemaître in 1932. [1] Changing from Schwarzschild to Lemaître coordinates removes the coordinate singularity at the Schwarzschild radius.
The transformation between Schwarzschild coordinates and Kruskal–Szekeres coordinates defined for r > 2GM and < < can be extended, as an analytic function, at least to the first singularity which occurs at =. Thus the above metric is a solution of Einstein's equations throughout this region.
There is no coordinate singularity at the Schwarzschild radius (event horizon). The outgoing ones are simply the time reverse of ingoing coordinates (the time is the proper time along outgoing particles that reach infinity with zero velocity). The solution was proposed independently by Paul Painlevé in 1921 [1] and Allvar Gullstrand [2] in 1922.
Section of the Whitney umbrella, an example of pinch point singularity. In geometry, a pinch point or cuspidal point is a type of singular point on an algebraic surface. The equation for the surface near a pinch point may be put in the form (,,) = + []
The singularity at the center of a Schwarzschild black hole is an example of a strong singularity. Space-like singularities are a feature of non-rotating uncharged black holes as described by the Schwarzschild metric , while time-like singularities are those that occur in charged or rotating black hole exact solutions.
This potential looks like: [5] (,,) = + (), where is the coordinate radius, and are the test-particle's conserved energy and angular momentum respectively (constructed from the Killing vectors). To preserve cosmic censorship , the black hole is restricted to the case of a < 1 {\displaystyle a<1} .
Ad
related to: singularity in coordinates meaning in science project proposal pdf format